Remarks on absolutely star countable spaces

Yan-Kui Song

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1755-1762
  • ISSN: 2391-5455

Abstract

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We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming 2 ℵ 0 = 2 ℵ 1 , there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).

How to cite

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Yan-Kui Song. "Remarks on absolutely star countable spaces." Open Mathematics 11.10 (2013): 1755-1762. <http://eudml.org/doc/269037>.

@article{Yan2013,
abstract = {We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming \[2^\{\aleph \_0 \} = 2^\{\aleph \_1 \}\] , there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).},
author = {Yan-Kui Song},
journal = {Open Mathematics},
keywords = {Pseudocompactness; Star countable; Absolutely star countable; Centered Lindelöf; Linked-Lindelöf; pseudocompactness; star countable; absolutely star countable; centered Lindelöf; linked-Lindelöf},
language = {eng},
number = {10},
pages = {1755-1762},
title = {Remarks on absolutely star countable spaces},
url = {http://eudml.org/doc/269037},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Yan-Kui Song
TI - Remarks on absolutely star countable spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1755
EP - 1762
AB - We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming \[2^{\aleph _0 } = 2^{\aleph _1 }\] , there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).
LA - eng
KW - Pseudocompactness; Star countable; Absolutely star countable; Centered Lindelöf; Linked-Lindelöf; pseudocompactness; star countable; absolutely star countable; centered Lindelöf; linked-Lindelöf
UR - http://eudml.org/doc/269037
ER -

References

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